This thesis describes the development of a descriptive mathematical model to determine the optimum position of a single tower crane. The objective function of the model is that of minimization of total travel time necessary to complete all movements from the installation of the crane until it is dismantled and removed. Previous models which have been developed to determine optimum crane selection and location are categorized as simulation models, expert systems and mathematical models and three particular models are credited as making contributions to the problem of tower crane location. However, the model developed here overcomes many of the deficiencies exhibited by these models. In developing a model to determine optimum tower crane location, the characteristics of the construction site in which it will be placed and those of the crane itself must be considered separately. The most challenging and significant problem is in determining the total number of movements which will occur during the time when a particular crane is installed on a particular site. The method adopted was the application of a linear programming technique, the Simplex Method. Once the (computer) model had been developed a wide range of simulations were carried out to see if any general truth concerning the optimum layout could be evinced. The result of these simulations demonstrated that there are potentially significant savings to be made, in terms of the time to complete all movements, by locating the crane in the optimum position rather than in one where the maximum time to complete all movements occurs. Typical savings were in the order of 30% but situations where the time savings were in excess of 100% and even 200% were not uncommon. The layout configuration was shown to have very little influence on the magnitude of the minimum time to complete all movements. And these optimum positions were found to consistently occur at the site perimeter, very often at the corners, whilst the positions associated with the maximum times were consistently located internally. However, when the cost implications of locating the crane at the perimeter, which necessitates the use of a crane with a longer jib than would be necessary were the crane located internally, were taken into account, it was shown that, in terms of cost benefits, the cheaper option is to use the crane with a short a jib as is viable for the purposes of reaching the points the crane is required to service, and locate the crane internally. Finally, neural networks were shown to have potential as a tool to predict optimum crane location, but further work is needed to produce a working model.